Related papers: Approximated maximum likelihood estimation in mult…
We propose a computationally efficient random walk on a convex body which rapidly mixes and closely tracks a time-varying log-concave distribution. We develop general theoretical guarantees on the required number of steps; this number can…
Continuous determinantal point processes (DPPs) are a class of repulsive point processes on $\mathbb{R}^d$ with many statistical applications. Although an explicit expression of their density is known, it is too complicated to be used…
We develop a general framework for estimating the $L_\infty(\mathbb{T}^d)$ error for the approximation of multivariate periodic functions belonging to specific reproducing kernel Hilbert spaces (RHKS) using approximants that are…
The ability to generate samples of the random effects from their conditional distributions is fundamental for inference in mixed effects models. Random walk Metropolis is widely used to perform such sampling, but this method is known to…
In order to learn the complex features of large spatio-temporal data, models with large parameter sets are often required. However, estimating a large number of parameters is often infeasible due to the computational and memory costs of…
We introduce an approach based on mirror descent and sequential Monte Carlo (SMC) to perform joint parameter inference and posterior estimation in latent variable models. This approach is based on minimisation of a functional over the…
We consider a random walk in random environment with random holding times, that is, the random walk jumping to one of its nearest neighbors with some transition probability after a random holding time. Both the transition probabilities and…
Iterated conformal mappings are used to obtain exact multifractal spectra of the harmonic measure for arbitrary Laplacian random walks in two dimensions. Separate spectra are found to describe scaling of the growth measure in time, of the…
Empirical likelihood method has been applied to dependent observations by Monti (1997) through the Whittle's estimation method. Similar asymptotic distribution of the empirical likelihood ratio statistic for stationary time series has been…
We consider a one dimensional ballistic random walk evolving in a parametric independent and identically distributed random environment. We study the asymptotic properties of the maximum likelihood estimator of the parameter based on a…
In this thesis, we study three physically relevant models of strongly correlated random variables: trapped fermions, random matrices and random walks. In the first part, we show several exact mappings between the ground state of a trapped…
This paper deals with nonparametric maximum likelihood estimation for Gaussian locally stationary processes. Our nonparametric MLE is constructed by minimizing a frequency domain likelihood over a class of functions. The asymptotic behavior…
An MCMC simulation method based on a two stage delayed rejection Metropolis-Hastings algorithm is proposed to estimate a factor multivariate stochastic volatility model. The first stage uses kstep iteration towards the mode, with k small,…
We develop importance sampling based efficient simulation techniques for three commonly encountered rare event probabilities associated with random walks having i.i.d. regularly varying increments; namely, 1) the large deviation…
Variational methods are employed in situations where exact Bayesian inference becomes intractable due to the difficulty in performing certain integrals. Typically, variational methods postulate a tractable posterior and formulate a lower…
A general method to construct recombinant tree approximations for stochastic volatility models is developed and applied to the Heston model for stock price dynamics. In this application, the resulting approximation is a four tuple Markov…
The probability distribution p(l) of an atom to return to a step at distance l from the detachment site, with a random walk in between, is exactly enumerated. In particular, we study the dependence of p(l) on step roughness, presence of…
Variational inference is a general framework to obtain approximations to the posterior distribution in a Bayesian context. In essence, variational inference entails an optimization over a given family of probability distributions to choose…
We give sharp, uniform estimates for the probability that a random walk of n steps on the reals avoids a half-line [y,infinity) given that it ends at the point x. The estimates hold for general continuous or lattice distributions provided…
We propose moment-based variational inference as a flexible framework for approximate smoothing of latent Markov jump processes. The main ingredient of our approach is to partition the set of all transitions of the latent process into…